reserve U for Universe;
reserve x for Element of U;
reserve U1,U2 for Universe;

theorem
  for c1,c2 being Cardinal st c1 in card U & c2 in card U holds
  card bool [:c1,c2:] in U
  proof
    let c1,c2 be Cardinal;
    assume that
A1: c1 in card U and
A2: c2 in card U;
    reconsider c1,c2 as Element of U by A1,A2,CLASSES2:13;
    reconsider c = bool [:c1,c2:] as Element of U;
    card c in U by CLASSES4:29;
    hence thesis;
  end;
